Anecdotes abound in the Danish public debate about well-educated immigrants that are in jobs they are formally overqualified for. Using a 1995-2002 panel data set based on Danish registers, this study attempts to find out how large a problem immigrant overeducation is in the context of the Danish labor market. More specifically, three questions are posed: First, to what extent are immigrants overeducated and are they more likely to be so than native Danes? Second, why are some immigrants more likely to become overeducated than others? And finally, what are the consequences of overeducation for individual wages? The authors find that among wage earners with at least a vocational education or higher, 25 percent of male non-Western immigrants are overeducated. The same applies for 15 percent of native Danes. Particularly immigrants with a foreign-acquired education risk becoming overeducated - here the share is 30 percent among those with a vocational education or higher. The authors find that Danish labor market experience is extremely important in reducing the likelihood of becoming overeducated. Years spent in the country without accumulating labor market experience do not improve an individual's chances of an appropriate job-to-education match. In terms of earnings consequences, the study concludes that years of overeducation do increase wages for immigrants, but much less so than years of adequate education. This is also true for native Danes, but the relative penalty for overeducation is much larger for immigrants than for Danes.